What is the Greatest Common Factor of 1288 and 1302?

Greatest common factor (GCF) of 1288 and 1302 is 14.

GCF(1288,1302) = 14

We will now calculate the prime factors of 1288 and 1302, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1288 and 1302.

How to find the GCF of 1288 and 1302?

We will first find the prime factorization of 1288 and 1302. After we will calculate the factors of 1288 and 1302 and find the biggest common factor number .

Step-1: Prime Factorization of 1288

Prime factors of 1288 are 2, 7, 23. Prime factorization of 1288 in exponential form is:

1288 = 2³ × 7¹ × 23¹

Step-2: Prime Factorization of 1302

Prime factors of 1302 are 2, 3, 7, 31. Prime factorization of 1302 in exponential form is:

1302 = 2¹ × 3¹ × 7¹ × 31¹

Step-3: Factors of 1288

List of positive integer factors of 1288 that divides 1288 without a remainder.

1, 2, 4, 7, 8, 14, 23, 28, 46, 56, 92, 161, 184, 322, 644

Step-4: Factors of 1302

List of positive integer factors of 1302 that divides 1288 without a remainder.

1, 2, 3, 6, 7, 14, 21, 31, 42, 62, 93, 186, 217, 434, 651

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1288 and 1302. The biggest common factor number is the GCF number.
So the greatest common factor 1288 and 1302 is 14.

Also check out the Least Common Multiple of 1288 and 1302